Applied Mathematics/Laplace Transforms

The Laplace transform is an integral transform which is widely used in physics and engineering. Laplace transform is denoted as .

The Laplace transform is named after mathematician and astronomer Pierre-Simon Laplace.

DefinitionEdit

For a function f(t), using Napier's constant"e" and complex number "s", the Laplace transform F(s) is defined as follow:

 

The parameter s is a complex number:

  with real numbers σ and ω.

This   is the Laplace transform of f(t).

Examples of Laplace transformEdit

Examples of Laplace transform
function result of Laplace transform
  (constant)  
   
  (n is natural number)  
   
   
   
   
   
    (n>0)
  (Delta function)  
  (Heaviside function)  

Examples of calculationEdit

(1)Suppose   (C = constant)
 
 
 

(2)Suppose